Yes, I can roam freely in all the Union's states, use the same currency in most of them, use my cellphone with no roaming costs, have access to health care if needed... that's the result of imposing less regulation, not more.
I never need to think about import/export restrictions, immigration law, visas, exchange rates, phone contracts or medical insurance contracts.
It certainly deregulated my life. I feel less regulated on what I can do. It removed barriers. And that's really the only thing that matters.
I think it is extremely hard to argue that this was a case of the EU deregulating anything. What happened was the EU started to regulate more, which invalidated the regulations of states.
The EU is specifically the mechanism by which the countries streamline their legislative differences.
Perhaps I'm missing something.